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A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times

Published online by Cambridge University Press:  03 June 2015

Raimund Bürger ,
Pep Mulet  and
Luis M. Villada
Raimund Bürger*
Affiliation:
CI2MA, and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Pep Mulet*
Affiliation:
Departament de Matemàtica Aplicada, Universitat de València, Av. Dr. Moliner 50, E-46100 Burjassot, Spain
Luis M. Villada*
Affiliation:
CI2MA, and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
*
Corresponding author. Email: rburger@ing-mat.udec.cl
Email: mulet@uv.es
Email: lmvillada@ing-mat.udec.cl
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Abstract

Multiclass Lighthill-Whitham-Richards traffic models [Benzoni-Gavage and Colombo, Euro. J. Appl. Math., 14 (2003), pp. 587–612; Wong and Wong, Transp. Res. A, 36 (2002), pp. 827–841] give rise to first-order systems of conservation laws that are hyperbolic under usual conditions, so that their associated Cauchy problems are well-posed. Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws. These terms can be diffusive under certain circumstances, thus, in principle, ensuring the stability of the solutions. The purpose of this paper is to analyze the stability of these diffusively corrected models under varying reaction times and anticipation lengths. It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths, and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.

Keywords

35K6535L6576T9976E99Traffic flowmultispecies modelanticipation lengthreaction timediffusive correctionquasilinear system of second-order PDEsstabilitynumerical simulation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 5 , October 2013 , pp. 728 - 758
Copyright
Copyright © Global-Science Press 2013

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